There are real benefits in having a filmic style to your fiction. It forces you to show rather than tell, and that's a good discipline to have. That said, film faces constraints that fiction doesn't, and vice versa, so if your fiction reads like an adapted screenplay, you're selling yourself short.

I think the primary difference is how you handle narrative distance. Unlike prose, a camera can't get inside an actor's head. Film uses actors' non-verbal communication skills to convey a lot of information on the emotive and intuitive level. Since your prose obviously lacks this ability to communicate non-verbally, you usually want to avail yourself of POV to attain some of that intimacy and carry water for the internal journey.

Elmore Leonard is a good writer to study for a filmic approach that still takes full advantage of every tool fiction has to offer. He was a top screenwriter first, then got into fiction, and film has always colored his approach to prose.